A Statistical Learning Perspective on Semi-dual Adversarial Neural Optimal Transport Solvers

• URL: http://arxiv.org/abs/2502.01310v1
• Date: Mon, 03 Feb 2025 12:37:20 GMT
• Title: A Statistical Learning Perspective on Semi-dual Adversarial Neural Optimal Transport Solvers
• Authors: Roman Tarasov, Petr Mokrov, Milena Gazdieva, Evgeny Burnaev, Alexander Korotin,
• Abstract summary: In this paper, we establish upper bounds on the generalization error of an approximate OT map recovered by the minimax quadratic OT solver. While our analysis focuses on the quadratic OT, we believe that similar bounds could be derived for more general OT formulations.
• Score: 65.28989155951132
• License:
• Abstract: Neural network based Optimal Transport (OT) is a recent and fruitful direction in the generative modeling community. It finds its applications in various fields such as domain translation, image super-resolution, computational biology and others. Among the existing approaches to OT, of considerable interest are adversarial minimax solvers based on semi-dual formulations of OT problems. While promising, these methods lack theoretical investigation from a statistical learning perspective. Our work fills this gap by establishing upper bounds on the generalization error of an approximate OT map recovered by the minimax quadratic OT solver. Importantly, the bounds we derive depend solely on some standard statistical and mathematical properties of the considered functional classes (neural networks). While our analysis focuses on the quadratic OT, we believe that similar bounds could be derived for more general OT formulations, paving the promising direction for future research.

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